1. Field of the Invention
The present invention relates to a measurement method, a measurement apparatus, and a method of manufacturing an optical system.
2. Description of the Related Art
An interferometer has been conventionally employed in measuring the transmitted wavefront or reflected wavefront (optical characteristic) of an optical system. Since an interferometer can measure the wavefront of an optical system with high precision, it is suitable for measuring the wavefront of an optical system which requires precise control of its wavefront aberration. A projection optical system of an exposure apparatus which fabricates a micropatterned semiconductor device using photolithography is required to control its wavefront aberration on the order of sub-nanometers, so wavefront measurement using an interferometer is important, particularly in this optical system.
Also, in recent years, as the wavelength of the exposure light shortens, it is demanded to control not only the wavefront aberration of a projection optical system of an exposure apparatus but also (the influence of) flare attributed to the roughnesses of the refracting surface and reflecting surface (surface shape errors) of the optical system and the internal refractive index distribution of the optical material of the optical system. Note that flare is particularly generated due to small high-spatial-frequency undulation components of a surface shape error and the internal refractive index distribution of an optical element which constitutes the projection optical system. For this reason, to reduce such flare, it is necessary to measure a surface shape error and the internal refractive index distribution of an optical element which constitutes the projection optical system with high precision up to high-spatial-frequency components.
To measure and evaluate a surface shape error of an optical element and the transmitted wavefront of an optical system using an interferometer with high precision up to small high-spatial-frequency undulation components, it is important to separate a wavefront error (a so-called system error) unique to the interferometer (its optical system), and a shape error of a measurement target surface.
Japanese Patent Laid-Open No. 5-223537 proposes a method of separating a system error and a shape error of a measurement target surface. A wavefront average method of measuring the wavefronts a plurality of times by randomly displacing the measurement region on a measurement target surface, for example, has been proposed. A method of measuring the wavefront while a measurement target surface is rotated and shifted with respect to the optical axis of an interferometer, and separately calculating rotationally asymmetrical components and rotationally symmetrical components (to be referred to as the “rotation/shift method” hereinafter) has also been proposed.
When attention is paid to small high-spatial-frequency undulation components of the wavefront measured using an interferometer, their phase amplitudes are sufficiently small as compared with the wavelength of a light source used in the interferometer. In view of this, the conjugate relationships, via the interferometer (its optical system), of high-spatial-frequency undulation components of a wavefront error unique to the interferometer change depending on the shape of a measurement target surface, and the values of their phase amplitudes detected by a detection unit, in turn, change. In case of, for example, a Fizeau interferometer, when the distance between the Fizeau surface and the measurement target surface changes, that is, when the radius of curvature differs between individual measurement target surfaces, the optical path length from the Fizeau surface to the detection unit also changes. As a consequence, different phase amplitudes (phase amplitude characteristics) are detected in response to changes in the optical path length.
For this reason, to separate a wavefront error unique to the interferometer with high precision up to high-spatial-frequency undulation components, it is necessary to perform the wavefront average method or the rotation/shift method using a standard surface having the same radius of curvature as the measurement target surface (or using the measurement target surface) every time the measurement target surface (its shape) changes.
Unfortunately, although a plurality of wavefronts (wavefront data) to be averaged must be random in the wavefront average method, it is in practice very difficult to manufacture a reference surface compatible with variations in these wavefronts for each measurement target surface, limiting the shape of the measurement target surface. Even if such a reference surface can be manufactured, the number of times of averaging must be increased in proportion to the required calibration precision (i.e., the precision of separating a system error), considerably prolonging the measurement time.
Furthermore, both the wavefront average method and the rotation/shift method require a driving mechanism which drives measurement target surfaces having various sizes and shapes (e.g., rotationally symmetrical shapes and rotationally asymmetrical shapes) relative to the optical axis of the interferometer. The driving mechanism requires optimization of, for example, a shape error attributed to a driving error and gravitational deformation in response to a change in orientation for each measurement target surface, leading to complication of the apparatus configuration and an increase in the apparatus cost.